Helium is supplied in pressure tanks. If I have a 10 liter tank at 200 atmospheres of pressure, how many 3 liter balloons can I fill? (Assume the balloons are at one atmosphere)
To calculate the number of 3-liter balloons that can be filled using a 10-liter tank at 200 atmospheres of pressure, we need to consider the ideal gas law.
The ideal gas law formula is:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles of gas
R = Ideal gas constant
T = Temperature
In this case, we are assuming the temperature is constant, therefore we can rewrite the equation as:
PV = constant
Now, let's calculate the number of moles of helium gas present in the 10-liter tank at 200 atmospheres of pressure:
P1V1 = P2V2
Where:
P1 = Initial pressure (200 atmospheres)
V1 = Initial volume (10 liters)
P2 = Final pressure (1 atmosphere, assuming balloons are at atmospheric pressure)
V2 = Final volume (unknown - the number of balloons we want to find)
Using the formula, we can rearrange it to solve for V2:
V2 = (P1V1) / P2
Plugging in the values:
V2 = (200 atm * 10 liters) / 1 atm
V2 = 2000 liters
So, the total volume of helium gas available is 2000 liters.
Now, we can calculate the number of 3-liter balloons that can be filled:
Number of balloons = Total volume of helium gas / Volume of each balloon
Number of balloons = 2000 liters / 3 liters ≈ 666.67
Since we cannot have fractional balloons, the maximum number of 3-liter balloons that can be filled is 666 balloons.